"Open the book to page ninety-nine and read, and the quality of the whole will be revealed to you."
--Ford Madox Ford

Saturday, September 22, 2007

Ian Stewart's "Why Beauty Is Truth"

Ian Stewart is Professor of Mathematics at the University of Warwick and Director of its Mathematics Awareness Centre. His many books include From Here to Infinity, Nature’s Numbers, Does God Play Dice?, The Problems of Mathematics, and Letters to a Young Mathematician. His writing has appeared in New Scientist, Discover, Scientific American, and many newspapers in the U.K. and U.S.

Page 102 would give you a better idea of the overall style of the book, because the central character’s father commits suicide — by suffocating himself — on that page. More precisely, the suffocation is reported on that page. Page 98 would clue you in on a key piece of technical content, the impossibility of solving equations of the fifth degree algebraically. Page 99, to be frank, is a bit boring, though unavoidable because it details the early life of Évariste Galois, a pivotal figure in the whole tale.

Galois was a would-be French revolutionary, with a huge but unrecognised talent for mathematics, who was killed in a duel over a woman. His life’s work, which very nearly died with him, was the invention of a new branch of mathematics, which opened the door to a mathematical formulation of one of the most powerful ideas ever discovered: symmetry. Before Galois, the story is about the development of algebra; after Galois, it heads rapidly towards the frontiers of modern physics — relativity, quantum, theory, superstrings.

I’m not sure that any page, taken at random, can be representative of a book that follows four millennia of mathematical discoveries, starting in ancient Babylon and working its way through to the 21st Century. However, page 99 does make it clear that this is a “people” book, centred on the often remarkable lives of the innovators, ancient and modern, who placed symmetry at the core of science and mathematics. There are duels and murders and betrayals, sex scandals, a beheading ... if you thought mathematicians led dull lives, you’ll find this book a revelation.

The mathematics itself emerges naturally from the lives and concerns of these historical characters. And as it happens, page 99 records a key moment in that four-thousand-year tale:

In October 1823 ... soon after Évariste arrived [at the College de Louis-le-Grand, a preparatory school] the students refused to chant in the school chapel, and the young Galois saw at first hand the fate of would-be revolutionaries: a hundred pupils were promptly expelled. Unfortunately for mathematics, the lesson did not deter him... he was awarded first prize in Latin, but then he started to get bored. In consequence, the school insisted that he should repeat his classes to improve his performance, but of course this made him even more bored, and things went from bad to worse. What saved Galois from the slippery slope to oblivion was mathematics, a subject with enough intellectual content to retain his interest. And not just any mathematics: Galois went straight to the classics, Legendre’s Elements of Geometry. It was a bit like a modern physics student starting out by reading the technical papers of Einstein.